Multiple-scattering theory for mean responses in a plate with sprung masses

Diagrammatic multiple-scattering theory is applied to the case of an infinite homogeneous plate in flexure attached to a random distribution of sprung masses. This system is a prototypical example of a wave-bearing master structure with a locally reacting 'fuzzy' substructure. Results for mean fields are obtained from the first-order smoothing approximation, the Foldy average t-matrix approximation, and Soven's coherent-potential approximation. The study of mean-square responses is reserved to a later paper. It is found that the attenuation as calculated by Pierce et al. [J. Vib. Acoustics 117, 339-348 (1995)] differs from that of the multiple-scattering theory by a fractional amount which is small if the individual sprung masses are weak.